Vacuum polarization in the spacetime of charged nonlinear black hole

TL;DR

This paper derives and analyzes the approximate stress-energy tensor of a quantized scalar field in the spacetime of a charged nonlinear black hole, revealing new features and comparing with known solutions.

Contribution

It provides the first analytical and numerical analysis of the stress-energy tensor for a scalar field in charged nonlinear black hole spacetime, extending previous work on Reissner-Nordström black holes.

Findings

Analytical expressions relate the tensor to Reissner-Nordström geometry in certain limits.

Numerical results highlight differences between minimal and conformal coupling.

Novel features of the stress-energy tensor in nonlinear black hole backgrounds are identified.

Abstract

Building on general formulas obtained from the approximate renormalized effective action, the approximate stress-energy tensor of the quantized massive scalar field with arbitrary curvature coupling in the spacetime of charged black hole being a solution of coupled equations of nonlinear electrodynamics and general relativity is constructed and analysed. It is shown that in a few limiting cases, the analytical expressions relating obtained tensor to the general renormalized stress-energy tensor evaluated in the geometry of the Reissner-Nordstr\"{o}m black hole could be derived. A detailed numerical analysis with special emphasis put on the minimal coupling is presented and the results are compared with those obtained earlier for the conformally coupled field. Some novel features of the renormalized stress-energy tensor are discussed.